Formation of close-packed sphere arrays in V-shaped grooves

ABSTRACT

The present invention relates to the self-assembly of a spherical-morphology block copolymer into V-shaped grooves of a substrate. Although spherical morphology block copolymers typically form a body-centered cubic system (bcc) sphere array in bulk, the V-shaped grooves promote the formation of a face-centered cubic system (fcc) sphere array that is well ordered. In one embodiment, the (111) planes of the fcc sphere array are parallel to the angled side walls of the V-shaped groove. The (100) plane of the fcc sphere array is parallel to the top surface of the substrate, and may show a square symmetry among adjacent spheres. This square symmetry is unlike the hexagonal symmetry seen in monolayers of spherical domains and is a useful geometry for lithography applications, especially those used in semiconductor applications.

This application claims the benefit of U.S. provisional patentapplication Ser. No. 60/825,501, filed Sep. 13, 2006, the disclosure ofwhich is incorporated herein by reference in its entirety.

FIELD OF THE INVENTION

The present invention relates to generating ordered patterns havingsquare symmetry from a self-assembled block copolymer.

BACKGROUND OF THE INVENTION

Within the following document, reference is made to numerous documentsthat provide further information related to subject matter beingdiscussed. These references are listed at the end of the DetailedDescription of the Preferred Embodiments and are identified by numbersin brackets [X], where X is the numerical identifier of a pertinentdocument. These documents are incorporated by reference in theirentireties.

Self-assembled block copolymer thin films have attracted a great deal ofattention recently as templates for nanolithography [1-9]. A diblockcopolymer contains two immiscible polymer chains covalently bondedtogether and, on annealing, undergoes a microphase separation to formself-assembled periodic nanoscale domains. The domains can exist invarious morphologies depending on the volume fractions of the twoconstituents of the polymer, including spheres, cylinders, and lamellae.The domain size and period scale with the molecular weight, making thesematerials useful masks for nanofabrication. Thin films of blockcopolymers have been used to pattern semiconductor dot and antidotarrays [1,2], metal dots and nanowires [3-6], magnetic storage media[7], and devices, such as capacitors, memory cells, and transistors havebeen fabricated using block copolymer lithography [8-9].

Successful implementation of block copolymer (BCP) patterning depends onthe ability to control the morphology, orientation, and packing of thedomains. Block copolymer domain patterns typically have good short-rangeorder but lack long-range order. Long-range ordering has beenaccomplished by various approaches such as the application of externalelectrical fields [10,11], temperature gradients [12], shear fields[13], or by using chemically or topographically patterned substrates[14-21].

Most studies using patterned substrates have focused on the behavior ofa monolayer of spherical or in-plane cylindrical block copolymerdomains, or on short cylinders or lamellae oriented perpendicular to thesurface. In addition, block copolymers have been confined within certaingeometries such as pores or droplets [22-25], which introduce additionalboundary conditions and can promote block copolymer morphologies notfound in the bulk, such as the formation of concentric cylinders bylamellar block copolymers, or helical structures by cylindrical blockcopolymers.

As such, there has been difficulty obtaining block copolymer domainpatterns that have good long-range ordering without requiring complexcontrol or boundary conditions. There has been further difficultyobtaining additional geometries, such as square geometries, for blockcopolymer patterning. Accordingly, there is a need for a technique toobtain block copolymer domain patterns that have good long-rangeordering and provide for enhanced geometries for such patterns.

SUMMARY OF THE INVENTION

The present invention relates to the self-assembly of aspherical-morphology block copolymer into V-shaped grooves of asubstrate. Although spherical morphology block copolymers typically forma body-centered cubic system (bcc) sphere array in bulk, the V-shapedgrooves promote the formation of a face-centered cubic system (fcc)sphere array that is well ordered. In one embodiment, the (111) planesof the fcc sphere array are parallel to the angled side walls of theV-shaped groove. The (100) plane of the fcc sphere array is parallel tothe top surface of the substrate, and may show a square symmetry amongadjacent spheres. This square symmetry is unlike the hexagonal symmetryseen in monolayers of spherical domains and is a useful geometry forlithography applications, especially those used in semiconductorapplications. Further, the sphere size in the top layer of the blockcopolymer adjusts depending on the relationship between the periodicityof the block copolymer and the film thickness within the V-shapedgroove.

Those skilled in the art will appreciate the scope of the presentinvention and realize additional aspects thereof after reading thefollowing detailed description of the preferred embodiments inassociation with the accompanying drawing figures.

BRIEF DESCRIPTION OF THE DRAWING FIGURES

The accompanying drawing figures incorporated in and forming a part ofthis specification illustrate several aspects of the invention, andtogether with the description serve to explain the principles of theinvention.

FIG. 1( a) is an image of V-shaped grooves anisotropically etched in a(100) silicon substrate with a 400 nm period, according to oneembodiment of the present invention.

FIG. 1( b) is an image of a block copolymer film spun on V-shapedgrooves and then annealed at 140° C. for 72 hours where a blockcopolymer fills the grooves to leave a planar surface.

FIG. 2( a) illustrates a cross-section of fcc packed spheres within aV-shaped groove where the (111) close-packed plane of the spheres isparallel to the walls of the V-shaped groove.

FIG. 2( b) illustrates a top view of the fcc packed spheres of FIG. 2(a).

FIG. 2( c) illustrates a cross section of bcc packed spheres within aV-shaped groove where the (110) closest-packed plane of the spheres isparallel to the walls of the V-shaped groove.

FIG. 2( d) illustrates a top view of the bcc packed spheres of FIG. 2(c).

FIG. 3( a) is an image of a top view of films in V-shaped grooves wheresquare packing of the spheres is visible.

FIG. 3( b) is an image of a cross section of films in V-shaped grooveswhere a sphere array of 11 rows is visible.

FIG. 3( c) is an image of the block copolymer directly adjacent to thesurfaces of the V-shaped grooves where hexagonal arrangement of thespheres is visible.

FIG. 4( a) is an image of block copolymer films within V-shaped grooveswhere the number N of (100) layers of block copolymer spheres in thegroove is 1 (N=1) and the black scale bar represents 200 nm.

FIG. 4( b) is an image of block copolymer films within V-shaped grooveswhere the number N of (100) layers of block copolymer spheres in thegroove is 2 (N=2) and the black scale bar represents 200 nm.

FIG. 4( c) is an image of block copolymer films within V-shaped grooveswhere the number N of (100) layers of block copolymer spheres in thegroove is 3 (N=3) and the black scale bar represents 200 nm.

FIG. 4( d) is an image of block copolymer films within V-shaped grooveswhere the number N of (100) layers of block copolymer spheres in thegroove is 4 (N=4) and the black scale bar represents 200 nm.

FIG. 4( e) is an image of block copolymer films within V-shaped grooveswhere the number N of (100) layers of block copolymer spheres in thegroove is 5 (N=5) and the black scale bar represents 200 nm.

FIG. 5( a) is an image of a sphere array showing a close-packed spherearrangement on the top surface.

FIG. 5( b) is an image of a cross-section of the sample of FIG. 5( a)showing the non-epitaxial top layer above the fcc arrangement of thelower layers of spheres.

FIG. 6 is a graph of the number of layers of spheres plotted against athickness of the block copolymer film according to one embodiment.

FIG. 7 is an image showing a change in the number of rows in the toplayer of a sphere array from 4 to 5.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The embodiments set forth below represent the necessary information toenable those skilled in the art to practice the invention and illustratethe best mode of practicing the invention. Upon reading the followingdescription in light of the accompanying drawing figures, those skilledin the art will understand the concepts of the invention and willrecognize applications of these concepts not particularly addressedherein. It should be understood that these concepts and applicationsfall within the scope of the disclosure and the accompanying claims.

The present invention relates to the spherical morphology of blockcopolymers. The resulting structures are particularly useful inlithographic applications for forming arrays of discrete metal dots orlike shapes in various semiconductor processing applications. In oneembodiment, the present invention provides a spherical block copolymerconfined in a substantially V-shaped groove. The resulting structuredemonstrates a face-centered cubic system (fcc) sphere array, which isnaturally close-packed and may have a top surface that shows asubstantially square symmetry that may be useful in fabricating squarearrays of functional nanostructures. Such arrangements do not occur inmonolayers of spherical domains, which are generally restricted tohexagonal symmetry, or in bulk spherical block copolymers, whichtypically pack in a body-centered cubic system (bcc) structure.

In one embodiment, a set of V-shaped grooves is formed by anisotropicetching of a substrate, such as a (100) oriented silicon (Si) wafer orother single crystal substrate. Notably, the orientation of a wafersurface or a crystal plane of a material is identified herein usingMiller indices (hkl), as will be understood by those skilled in the art.A V-shaped groove is defined as any type of groove wherein the upper,opposing side walls of the groove are angled and form an angle less than180 degrees relative to one another. The bottom of the V-shaped groovedoes not need to come to a defined point. The bottom of the “V” may beflat, curved, or formed from additional walls.

In this embodiment, a tri-layer resist stack containing anantireflective coating, silica, and a photoresist is deposited onto a Sisubstrate that has been coated with 30 nm of silicon nitride. A gratingimage is recorded in the photoresist using a Lloyd's Mirror interferencelithography system [26] with a 325-nm-wavelength helium-cadmium laser.The period of the grating is varied between 400 and 200 nanometers (nm)by changing the angle of incidence of the expanded laser beam on thesubstrate and an adjacent mirror. Achromatic interference lithography isemployed to pattern 100 nm periodic gratings [27]. The periodic gratingstructure in the developed photoresist is transferred through thenitride layer by a series of reactive-ion-etching steps.

After etching, the remaining tri-layer resist stack is removed by aresist stripper, such as EKC265, at 70° C., followed by oxygen plasma.The Si substrate is then dipped into buffered hydrofluoric acid,immediately prior to etching the silicon in 25% Potassium Hydroxide(KOH) at 40° C. with ultrasonic agitation. After the silicon etch, thenitride mask is removed by hydrofluoric acid solution and cleaned byoxygen ashing. In this example, the resulting V-shaped grooves in the Sisubstrate have widths varying from 50 to 290 nm, as illustrated in thephotograph of FIG. 1( a). A native silicon oxide layer having athickness of approximately two to three (2-3) nm is present on thegroove walls.

Continuing with the example, a spherical-morphology polystyrene(PS)-block-polyferrocenyldimethylsilane (PFS) block copolymer [28], witha molecular weight of 32 kg/mol for PS and 10 kg/mol for PFS, is spincoated from 1.5 weight % toluene solution onto the grooved substrates,where the thickness is controlled by the spin speed. Micro-phaseseparation is carried out by an annealing process under vacuum at 140°C. for 72 hours. During annealing, the block copolymer flows into thegrooves, resulting in a planar film that partially or completely fillsthe grooves, as illustrated in FIG. 1( b). Preferably, the mesas betweenthe grooves are left free from the block copolymer.

To actually view the arrangement of the PFS spheres on the top surfaceor the cleaved cross-section, the substrate may be subjected to deep-UVexposure and the PS matrix may be partially etched by an oxygen plasma.Additionally, the domain arrangement at the flat surfaces of the groovesmay be exposed by first applying hot melt glue to the top surface of thesample and then etching away the entire Si substrate in 25% KOH solutionto leave triangular prisms of block copolymer attached to the glue thatcould be viewed from the side.

The present invention provides a unique geometrical packing of the PFSspheres within the V-shaped grooves. In one embodiment, the two sidewalls of the V-shaped grooves are formed by the (111) planes of the Sisubstrate and have an intersection angle of about 70.6°. When theintersection is about 70.6°, the symmetry of the top surfaces of thesphere array is substantially square. If this angle is varied, thesymmetry becomes rectangular. For example, an intersection at an angleof 90° provides a very rectangular symmetry. An fcc sphere array A canbe accommodated within such a V-shaped groove V, as shown in FIGS. 2( a)and 2(b). For a V-shaped groove with an intersection angle of 70.6°, the(111) and (11 1) planes of the sphere array A are parallel to the twoside walls for the V-shaped groove V, the (001) plane is parallel to theSi substrate, and the ( 110) plane is perpendicular to the length of theV-shaped groove. FIG. 2( b) shows that the top surface of the fcc spherearray A has a square symmetry, while the cross-section of FIG. 2( a)shows that layers of spheres in the sphere array A are substantiallyparallel to the surface of the Si substrate and correspond to theparallel (001) planes. In comparison, for bcc packing in the sameV-shaped groove V, if the closest-packed plane (110) lies parallel to agroove wall, as illustrated in FIG. 2( c), then the top surface of thesphere array will have a distorted hexagonal arrangement, as shown inFIG. 2( d).

FIG. 3( a) shows a top view and FIG. 3( b) shows a cross-section of anetched sphere array. The top surface shows a square symmetry in thesphere packing, and the cross-section shows 11 rows of spheres whereeach row is substantially parallel to the surface of the Si substrate.This arrangement is consistent with the fcc packing shown in FIGS. 2( a)and 2(b). For the block copolymer in this example, the averagecenter-to-center distance in a close-packed monolayer of spheres isp₀=28.6 nm, and the spacing between two parallel close-packed rows in amonolayer of spheres is d₀=24.8 nm. On the basis of 3D fcc packing, aspacing of t_(o)=√{square root over (2)}d₀/√{square root over (3)}=20.25nm is expected between the rows of spheres in the cross-sectional imageof the sphere array in the V-shaped groove. This is in agreement withthe average interlayer spacing (excluding the top layer) of 20.5 nmmeasured from the cross-sectional image, FIG. 3( b). This confirms thatthe PFS spheres are packed in an fcc arrangement. FIG. 3( c) shows aside view of the block copolymer in a V-shaped groove after removal ofthe substrate and viewed at an angle from the normal to show one surfaceof the block copolymer prisms. The hexagonal arrangement of domains thatcan be seen on the surfaces of the block copolymer (i.e., in contactwith the original groove surfaces) is consistent with the (111) planesof fcc packing.

Although the block copolymer of the primary example is PS-PFS, otherblock copolymer combinations are applicable. Exemplary block copolymersinclude, but are not limited to polystyrene-b-poly(methyl methacrylate)(PS-PMMA), polystyrene-b-poly(dimethyl-siloxane) (PS-PDMS),polystyrene-b-poly(2-vinyl pyridine) (PS-P2VP),polystyrene-b-polybutadiene (PS-PB), andpolystyrene-b-polybutadiene-b-poly(methyl methacrylate) (PS-PB-PMMA).

Previous work has shown that spherical-morphology block copolymers formbcc structures in the bulk, with fcc expected only under very limitedconditions of composition, segment interaction parameter, and chainlength [29]. However, close-packing is typically found in thin filmsconsisting of a monolayer of spheres [30]. In films with two or threelayers, close-packing has also been found [31], but in films with alarger number of layers, bcc packing has been observed with the (110)plane parallel to the substrate [32-33]. For example, PS-P2VP films withsix layers of spheres showed a bcc structure [32]. In the currentexample, it is likely that the geometrical constraint of the V-shapedgrooves would stabilize the fcc arrangement even to relatively thickfilms.

The effect of block copolymer film thickness on the structure of the PFSsphere array is now described. For the smallest V-shaped grooves withthe thinnest films, a single row of spheres may be formed in theV-shaped groove as shown in FIG. 4( a). In this sample, the filmthickness, which is measured from the intersection point of the twosides of the V-shaped groove to the top of the sphere in thecross-sectional view, is 36-40 nm. A 73-nm-thick film shows a two-layerarrangement where the second layer of spheres is offset from the spheresin the first row and has a square arrangement, as illustrated in FIG. 4b. FIGS. 4( c), 4(d), and 4(e) show arrangements of 3, 4, and 5 layers,respectively, which are formed in deeper grooves. The top layer ofspheres again has a square arrangement, but its sphere diameter is oftensmaller than that of the lower layers. In addition, the spacing betweenthe top layer of spheres and the layer immediately below may differ fromthe average spacing between layers. The same behavior may be seen inthicker films, such as that provided in FIG. 3. For example, films thatare 216-229 nm thick may consist of 10 layers of spheres, whereas filmsthat are ˜230-240 nm thick may have an additional layer of smallerspheres, and films that are ˜240-255 nm thick may consist of 11 layersof approximately uniform spheres.

In some cases, the existence of a close-packed sphere arrangement on thetop surface of the V-shaped groove is observed, as shown in FIGS. 5( a)and 5(b). In this example, the cross-sectional image of FIG. 5( b)indicates that the lower layers are in an fcc arrangement, but the topview of FIG. 5( a) indicates that the top layer of spheres is no longerepitaxial with the underlying structure and contains 12 rows of spheres.The top layer packing is identical to that seen in a close-packedmonolayer of spheres templated by a shallow, vertical-walled trench[29-34].

The size and number of spheres in the top layer of the fcc array may becontrolled. To quantify the sphere arrangement on top of and within thefcc array, a plot of the number of layers of spheres seen in thecross-sectional images versus the block copolymer film thickness isprovided in FIG. 6. This thickness is divided by t_(o)=20.46 nm, whichis the average spacing between layers in the cross-sectional projectionmeasured from all samples while excluding the spacing between the topand second layers in those samples with a smaller sphere diameter in thetop layer. Two sets of data points are plotted. Solid points representsamples in which the diameter of the top-layer spheres is similar tothat of underlying layers. In these samples, the top layer was usuallyhexagonally arranged, and therefore nonepitaxial with the underlying fccarray, as in FIG. 5( a), although some samples showed a squaresymmetric, epitaxial top layer, as in FIG. 4( b) or 4(e). These datapoints form a “staircase” plot in which a given integer number oflayers, N, can be found in films within a thickness range ofapproximately (N+0.5)t_(o) to (N+1.5)t_(o). The second set of datapoints, shown with open symbols, represents arrays where the spheres ofthe top layer are significantly smaller than the underlying spheres. Inthis case, a fractional layer number was calculated as the ratio of theprojected area of the top layer of spheres to that of the underlyingspheres in the cross-sectional image. All of these samples showsquare-symmetric, epitaxial top layers. The data points are clusteredbetween the horizontal sections of the staircase plot.

A solid line, corresponding to a slope of 1.0, is fitted through thesolid data points. This intersects the x axis at a thickness of0.99t_(o). The nonzero intercept is due to the presence of the brushlayer at the surfaces of the grooves. The PFS block preferentially wetsthe surfaces of the groove [34], which are covered by a thin nativeoxide layer, leading to an offset of the first layer of spheres abovethe lowest part of the V-shaped groove, as indicated in the inset ofFIG. 6. Films thinner than ˜t_(o) are expected to contain only of abrush layer and would not show a well-developed sphere morphology.

These results show that the block copolymer can fill the V-shapedconfinement in different ways depending on the relationship between theblock copolymer film thickness and the periodicity of the sphericaldomains. The geometry of the V-shaped groove promotes an fcc packing ofthe spheres, which conforms exactly to the angle of the groove. If thefilm thickness is close to an integer number of (100) fcc sphere layers,then a well-ordered fcc structure is expected to form. However,deviations from exact commensurability can be accommodated in two ways:either by the formation of a top fcc layer with a different spherediameter and thickness, or by a change in the packing of the top layerthat maintains, approximately, the sphere diameter, but leads todefective packing such that the top layer is no longer epitaxial withthe underlying fcc sphere array. For instance, the example of FIGS. 5(a) and 5(b) exhibits the latter case, where the loss of epitaxy in thetop layer has allowed an additional row of spheres to be present in thetop layer. The coexistence of these two types of morphology in thisblock copolymer system suggests that the energy differences between themare modest, though the formation of the smaller-diameter epitaxialspheres appears to dominate when the film thickness is furthest fromcommensurability.

Finally, FIG. 7 shows the coexistence of different top-layer spherearrangements within a groove. This sample shows a change from four rowsof spheres to five, with the introduction of a defect in the top,nonepitaxial layer of spheres. The behavior of this spherical-morphologyPS-PFS block copolymer shows interesting parallels with the packing ofthe same block copolymer in shallow, vertical-walled trenches [34]. Forthe same PS-PFS block copolymer arranged in a shallow trench, awell-ordered close-packed monolayer of spheres is observed for allgroove widths up to approximately 13d_(o) (˜320 nm), beyond whichlong-range order breaks down. In the ordered monolayer, the row spacingadjusts such that an integer number of rows of block copolymer spheresforms within the groove, leading to a staircase-shaped plot of number ofrows of spheres versus groove width, but for all groove widths thesphere array is close-packed with hexagonal (or slightly distortedhexagonal) packing. In contrast, the block copolymer confined within theV-shaped groove does not adjust its interlayer spacing t₀ within thebulk of the V-shaped groove, and incommensurabilities are insteadaccommodated by changes in packing, or changes in sphere diameter, whichare restricted to the top layer of spheres. Thus, the top layer ofspheres may show a hexagonal arrangement or a square arrangement. It issignificant that the groove geometry promotes an fcc sphere array evenfor relatively thick films, despite the bulk morphology being bcc.

As a further comparison, colloidal spheres, such as silica or latex,assembled in V-shaped grooves also show fcc packing with asquare-symmetric top layer [35-38], which is superficially similar tothat of the block copolymer spheres, though on a much larger lengthscale. However, if the number of spheres available does not form aninteger number of layers, then partial layers are created, containingvacancies. In the block copolymer case, the local density of the blockcopolymer remains constant and the system cannot form “vacancies,” sothe incommensurability must be accommodated by adjustment of the spheresize or the packing structure.

The square array formed by the fcc-packed block copolymer may have usesin block copolymer lithography or other device applications where asquare array of nanostructures is required. A pattern transfer method,such as nano-imprinting, may be used. For example, an imprint stamp froman etched PS-PFS block copolymer film may be made by coating the filmwith a conformally sputtered 7-nm-thick silica layer and then stampingit into a polymethyl methacrylate (495 kg/mol) resist layer with apressure of 150 MPa at 110° C. for 3.5 hours. This leads to an imprintedpattern in the resist corresponding to the topography of the top layerof PFS domains.

In conclusion, a spherical block copolymer is formed within V-shapedgrooves of a substrate to form an fcc sphere array because of thegeometric constraints of the V-shaped grooves. Within the fcc spherearray, the close-packed (111) planes are parallel to the walls of theV-shaped grooves, and the top surfaces of the fcc sphere array are onthe (100) plane and have square symmetry. The top layer of spheresadjusts its structure depending on the commensurability between thethickness of the block copolymer and the (100) plane spacing. Either thesphere diameter adjusts within the top layer while maintaining the fccepitaxy, or the top layer of spheres may lose its epitaxial relationwith the underlying fcc lattice and instead form a close-packed layer.This behavior differs from that of colloidal sphere packing, whichexhibits vacancies in the structure if the top layer of spheres isincomplete. The square symmetry of the top layer of the fcc blockcopolymer sphere array may provide a useful template for making squarearrays of nanostructures. The ability to form ordered 3D arrangementsfor a range of film thicknesses makes block copolymers attractive forthe fault-tolerant templated self-assembly of nanoscale periodic arrays.

Those skilled in the art will recognize improvements and modificationsto the preferred embodiments of the present invention. All suchimprovements and modifications are considered within the scope of theconcepts disclosed herein and the claims that follow.

REFERENCES

Documents cited above, which are incorporated herein by reference intheir entireties:

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1. A method comprising: providing a substrate having at least oneV-shaped groove formed at least in part by two angled side walls; andapplying a self-assembling block copolymer in the at least one V-shapedgroove, an angle of the walls for the at least one V-shaped groove andthe block copolymer selected such that the block copolymer forms aface-centered cubic system (fcc) sphere array of close-packed sphereswithin the at least one V-shaped groove.
 2. The method of claim 1wherein the providing the substrate further comprises etching the atleast one V-shaped groove in the substrate.
 3. The method of claim 1wherein the at least one V-shaped groove is etched in a (100) orientedsubstrate wherein (100) is a Miller index.
 4. The method of claim 1wherein the at least one V-shaped groove is formed by (111) orientedplanes of the substrate wherein (111) is a Miller index.
 5. The methodof claim 4 wherein an angle formed by the two angled side walls is about70.6 degrees.
 6. The method of claim 1 wherein the substrate is asilicon wafer.
 7. The method of claim 1 wherein the substrate comprisesa plurality of V-shaped grooves including the at least one V-shapedgroove, and mesas are provided on a top surface of the substrate betweenadjacent ones of the plurality of V-shaped grooves.
 8. The method ofclaim 7 wherein the fcc sphere array of close-packed spheres formed ineach of the plurality of V-shaped grooves does not cover the mesas. 9.The method of claim 1 wherein the fcc sphere array of close-packedspheres maintains order throughout the at least one V-shaped groove. 10.The method of claim 1 wherein respective (111) and (11 1) orientedplanes of the fcc sphere array of close-packed spheres are parallel tothe two angled side walls of the at least one V-shaped groove, andwherein (111) and (11 1) are Miller indexes.
 11. The method of claim 1wherein a (001) oriented plane of the fcc sphere array of close-packedspheres is parallel to a top surface of the substrate, and wherein (001)is a Miller index.
 12. The method of claim 1 wherein a ( 110) orientedplane of the fcc sphere array of close-packed spheres is perpendicularto a length of the at least one V-shaped groove, and wherein ( 110) is aMiller index.
 13. The method of claim 1 wherein a top layer of spheresin the fcc sphere array of close-packed spheres provides a substantiallysquare symmetry among adjacent spheres of the sphere array.
 14. Themethod of claim 1 wherein a diameter of spheres in a top layer ofspheres in the fcc sphere array is smaller than a diameter of spheres inunderlying layers of spheres in the fcc sphere array.
 15. The method ofclaim 1 wherein a top layer of spheres in the fcc sphere array loses anepitaxial relationship with underlying layers of spheres in the fccsphere array.
 16. The method of claim 1 wherein the fcc sphere arraycomprises a plurality of layers of spheres.
 17. The method of claim 16wherein the fcc sphere array comprises more than three layers ofspheres.
 18. The method of claim 1 wherein for the at least one V-shapedgroove, the two angled side walls come to a point at a bottom of the atleast one V-shaped groove.
 19. The method of claim 1 wherein theself-assembling block copolymer is a diblock copolymer.
 20. The methodof claim 1 wherein one block of the block copolymer comprises at leastone of polystyrene, polyferrocenyldimethylsilane, poly(methylmethacrylate), poly(dimethyl-siloxane), poly(2-vinyl pyridine), andpolybutadiene.
 21. The method of claim 1 wherein the block copolymer hasa spherical morphology.